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ANALYTICAL MECHANICS
respect to the time.   Differentiating (3) we obtain dr
=        ,      _
~ r dt     r dt
'entiating (4) we get
de
(5)
= y cos 6  x sin 6. components satisfy the relation
0 = Vf2+r202.
(6) (7)
ILLUSTRATIVE EXAMPLE. Article describes the motion defined by the equations
x  a cos kt,                                               (a)
y = a sin kt.                                        (b)
.e equation of the path, the velocity at any instant, and the com-i of the latter.
.ring and adding (a) and (b) we eliminate t and obtain x* + ?/ = a2
equation of the path. Teutiating (a), we have
x = ~
=  ka sin kt = Joy.
rentiating (b), we obtain
y = dft
= ka cos kt                                  ^
= kx-                                               FIG. 51.